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Suppose a device has three independent components, all of whose lifetimes (in months) are modeled by the exponential
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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
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- Suppose that you decide to fit a logistic regression model using these data. Let Y = 1 if a subject develops cancer and 0 otherwise. Let Finasteride = 1 if a subject received Finasteride and 0 if they received placebo. The estimated logistic model is What is the value of ?arrow_forwardA catalog company builds a logistic regression (LR) model to predict the probability that a customer will buy from the catalog during a particular campaign (mailing). The LR model contains 2 independent variables: X1 spend per year in 1000's of dollars (so $2000 will be coded as X1 2) and X2= does customer possess a loyalty card (X2 1 means customer has loyalty card, X2 = 0 means customer does not have the card). Once the model is fitted, the LR coefficients are provided below: = Constant term (BETAO): - 3.5 (negative 3.5) X1 coeff. (BETA1): 0.6 X2 coeff.(BETA2): 1.5 What is the probability that a customer who spends $6000/year and who does NOT have a loyalty card will respond to the campaign? = O About 53% O About 15% About 33% O About 45%arrow_forwardYou are an econometrician working in the Ministry of Finance in Trinidad and Tobago and using a database consisting of 108 monthly observations on automobile accidents for Trinidad and Tobago between January 2011 and December 2019, you estimate the following model: log( totacc,) = Bo + Bit+ B2feb, + Bzmar. + B12 dec, + 4, where totacc is the total number of accidents, t is time (measured in months), and feb, mar,, dec, are dummy variables indicating whether time period t corresponds to the appropriate month. You obtain the following OLS results: 108 31.06 0.0000 Source I df MS Number of obs F( 12, Prob > F R-squared Adj R-squared = 0.7712 95) Model I Residual I 1.00244071 12 .083536726 .255496765 95 .00268944 0.7969 Total | 1.25793748 107 .011756425 Root MSE .05186 ltotacc I Coef. Std. Err. P>It| [95% Conf. Interval] t .0027471 .0001611 17.06 -1.75 3.26 0.000 .0024274 .0030669 0.084 0.002 .0058479 .1283621 -.0912208 .031287 -.030058 -.0164521 -.0283678 -.0109886 .0053981 -.0062397 feb…arrow_forward
- Can gender, educational level, and age predict the odds that someone votes for a particular candidate in the election? Over 1500 voters were selected, and data were col-lected on the highest year of school completed, their age, and their gender. We wish to t a logistic regression model: log(1 p p ) = 0 + 1Age + 2Education + 3Gender, where p is the binomial probability that a person voted for candidate Johnson, and gender is coded as the indicator for female. The R output is given below. parameter df estimate s.e z p-value (Intercept) 1 .1119 .3481 .321 .748 Age 1 .0020 .0032 .613 .54 Education 1 -.0100 .0184 .547 .585 Gender 1 .4282 .1040 4.117 .000 Null deviance: 255.95 on 1499 degrees of freedom Residual deviance: 220.80 on 1496 degrees of freedom Write down the tted logistic regression and give a short summary about the data analysis . Calculate the probability of voting for Johnson for a…arrow_forwardAn investigator modeled the log-odds of getting stomach cancer as a function of number of servings of vegetables per week and the number of servings of red mean per week using logistic regression. The odds that a person gets stomach cancer if they have 4 servings of red meat a week are 1.2 times the odds of cancer for someone who has 3 servings of red meat a week. Suppose the fitted regression model is given as log-odds = -6 + 0.182 M – 0.105 V, where M = #servings of red meat per week and V = #servings of vegetables per week. What is the odds ratio representing the change in odds for an increase in one serving of vegetables? Give the answer to three decimal places.arrow_forwardConsider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.arrow_forward
- Consider the logit regression log(odds(QualExam) = ßo + B, • ParEduc + B, • Awards. where QualExam is a binary variable that indicates passing the exam if equal to 1, and failing the exam if 0, ParEduc indicates the parents' education level, and Awards is a binary variable that indicates having experience of obtaining award(s) if equal to 1, and not having experience if 0. Given the parents' average education level unchanged, the odds ratio is expected to be _ for an individual with awards to pass the exam comparing to those without awards. For an individual without awards and the parents' education level of 4, the estimated probability of passing the exam is approximately_. ParEduc Awards Intercept -10.53 2.98 0.48 O A. 0.48; 80%. O B. 1.616; 80%. O C. 1.616; 4%. O D. 0.48; 4%.arrow_forwardIn a study of 31 patients with esophageal cancer, it was found that in 18 of the patients the cancer had metastasized to the lymph nodes. Thus an overall estimate of the probability of metastasis is 0.58. A predictor variable measured on each patient is Size of the tumor (in cm). A fitted logistic regression model is 18 31 log p(z) (1-p(z) =-2.4+0.6x= -2.4+0.6- Size p(z) 1-p(z)' (a) Use this model to estimate the odds of metastasis. if a patient's tumor size is 4 cm. (b) Use the model to predict the probability of metastasis if a patient's tumor size is 4 cm. (c) How much do the estimated odds change if the tumor size changes from 4 cm to 5 cm? (d) How much does the estimate of p(z) change if the tumor size changes from 4 cm to 5 cm? (e) How large does a tumor need to be for the estimated probability of metastasis to be at least 0.90?arrow_forwardEnvironmental conditions can affect the growth of coral. To study this, a researcher examined a species of coral that is found in the Caribbean Sea and the Gulf of Mexico. At 12 localities, he determined the average annual calcification rate of coral over a period of several years and the average annual maximum sea surface temperature during the same period. Calcification rate affects the growth of coral, with higher rates corresponding to greater growth. The table contains data for these 12 localities. Maximum sea surface temperature (°C) and calcification rate (g cm² yr¯¹) Maximum Sea Surface Temperature 29.4 29.4 29.4 29.6 29.1 28.7 Calcification Rate 1.48 1.53 1.52 1.48 1.31 1.25 Maximum Sea Surface Temperature 29.7 29.5 29.4 29.0 29.0 29.0 Calcification Rate 1.63 1.53 1.46 1.24 1.29 1.12 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! The residuals for average annual maximum sea surface…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
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